Ex 13.9, 1 (Optional)
A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see Fig. 13.31). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.
From figure,
length and height of all open portions are same
Let length of open portion be l
and height of open portion be h
Now,
Height of book shelf = 3 × Height of open portion + 4 × Thickness of plank
110 = 3h + 4 × 5
110 = 3h + 20
3h = 110 − 20
3h = 90
h = 90/3 = 30 cm
And,
Length of Bookshelf = Length of open portion
+ 2 × Thickness of plank
85 = l + 2 × (5)
85 = l + 10
85 – 10 = l
l = 75 cm
Now,
Area of bookshelf to be polished
= TSA of external bookshelf − 3 × Area of Open Portion
Area of open portion will be the area of rectangle with length 75 and breadth 30
Area of open portion will be the area of rectangle with length 75 and breadth 30
= 2 (14225) − 6750
= 28450 − 6750
= 21700 cm2
Now,
Cost of polishing 1 cm2 = 20 paise
Cost of polishing 21700 cm2 = 20 × 21700
= 434000 paise
= Rs 434000/100
= Rs 4340
Now,
We need to paint the inner surface
Total Area to be painted
= 3 × (Total Surface area of internal of shelf − Area of Open Portion)
= 3 × (2 (30 × 75 + 75 × 20 + 20 × 30) − (30 × 75)
= 3 × (2 (2250 + 1500 + 600) − (2250))
= 3 × (2 × (4350) − 2250)
= 3 × (8700 − 2250)
= 3 × (6450)
= 19350 cm2
Now,
Cost of painting 1 cm2 = 10 paise
Cost of painting 19350 cm2 = 19350 × 10
= 193500 paise
= Rs 193500/100
= Rs 1935
Total Expenses = Cost of Polishing + Cost of Painting
= 4340 + 1935
= Rs 6275

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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